Fagnano Orbits of Polygonal Dual Billiards

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Abstract

Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.

Original languageEnglish (US)
Pages (from-to)279-286
Number of pages8
JournalGeometriae Dedicata
Volume77
Issue number3
DOIs
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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